get a money order then mail it along with a deposit slip to your bank. that's what I do as my bank is in TX and I live in OR

See if your bank offers mobile deposit. You can deposit checks by taking a picture of them with your phone. You cannot deposit cash this way.

Do on online transfer. Call your bank or wire it in.

Does your bank's mobile app allow you to make a deposit by talking a picture of the check?

If under a certain amount, typically $1000, most large banks have this option

I worked for a bank some 25 years ago, before online banking. When a customer needed to make a deposit while out of town/state where we did not have branches, they mailed the deposit. Checks were endorsed with "For deposit only to account number xxx" while cash had to be changed into a money order, made out to the person depositing the money and endorsed "For deposit only to account number xxx". I can't remember anymore if the check/money order had to be accompanied by a deposit slip or not.

Anyway, you can call your bank to see if that procedure is still available and where to mail the check/money order to. Of course it's going to take a few days for the check/money order to get deposited but you could overnight it which would speed up the process.

DEBS is mistaken. Unless there is a specific agreement between the banks involved, one bank CANNOT accept deposits for another bank. AT BEST, they could do a wire transfer, but that will cost more than you want to pay.

Make your deposit BEFORE you leave, or find an ATM that accepts deposits for your bank.

If it's a check you can use your bank's mobile app. Even small credit unions allow you to scan checks from your phone these days to deposit them.

If it's cash, you can go to another bank and speak with them about it. There may be a fee, but as long as you know you account number and routing number they can do it. (Get those numbers off your bank's website after you login.)